The least-control principle for learning at equilibrium
- URL: http://arxiv.org/abs/2207.01332v1
- Date: Mon, 4 Jul 2022 11:27:08 GMT
- Title: The least-control principle for learning at equilibrium
- Authors: Alexander Meulemans, Nicolas Zucchet, Seijin Kobayashi, Johannes von
Oswald, Jo\~ao Sacramento
- Abstract summary: We present a new principle for learning equilibrium recurrent neural networks, deep equilibrium models, or meta-learning.
Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.
- Score: 65.2998274413952
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: Equilibrium systems are a powerful way to express neural computations. As
special cases, they include models of great current interest in both
neuroscience and machine learning, such as equilibrium recurrent neural
networks, deep equilibrium models, or meta-learning. Here, we present a new
principle for learning such systems with a temporally- and spatially-local
rule. Our principle casts learning as a least-control problem, where we first
introduce an optimal controller to lead the system towards a solution state,
and then define learning as reducing the amount of control needed to reach such
a state. We show that incorporating learning signals within a dynamics as an
optimal control enables transmitting credit assignment information in
previously unknown ways, avoids storing intermediate states in memory, and does
not rely on infinitesimal learning signals. In practice, our principle leads to
strong performance matching that of leading gradient-based learning methods
when applied to an array of problems involving recurrent neural networks and
meta-learning. Our results shed light on how the brain might learn and offer
new ways of approaching a broad class of machine learning problems.
Related papers
- A Unified Framework for Neural Computation and Learning Over Time [56.44910327178975]
Hamiltonian Learning is a novel unified framework for learning with neural networks "over time"
It is based on differential equations that: (i) can be integrated without the need of external software solvers; (ii) generalize the well-established notion of gradient-based learning in feed-forward and recurrent networks; (iii) open to novel perspectives.
arXiv Detail & Related papers (2024-09-18T14:57:13Z) - Simple and Effective Transfer Learning for Neuro-Symbolic Integration [50.592338727912946]
A potential solution to this issue is Neuro-Symbolic Integration (NeSy), where neural approaches are combined with symbolic reasoning.
Most of these methods exploit a neural network to map perceptions to symbols and a logical reasoner to predict the output of the downstream task.
They suffer from several issues, including slow convergence, learning difficulties with complex perception tasks, and convergence to local minima.
This paper proposes a simple yet effective method to ameliorate these problems.
arXiv Detail & Related papers (2024-02-21T15:51:01Z) - A minimax optimal control approach for robust neural ODEs [44.99833362998488]
We address the adversarial training of neural ODEs from a robust control perspective.
We derive first order optimality conditions in the form of Pontryagin's Maximum Principle.
arXiv Detail & Related papers (2023-10-26T17:07:43Z) - NeuralFastLAS: Fast Logic-Based Learning from Raw Data [54.938128496934695]
Symbolic rule learners generate interpretable solutions, however they require the input to be encoded symbolically.
Neuro-symbolic approaches overcome this issue by mapping raw data to latent symbolic concepts using a neural network.
We introduce NeuralFastLAS, a scalable and fast end-to-end approach that trains a neural network jointly with a symbolic learner.
arXiv Detail & Related papers (2023-10-08T12:33:42Z) - Control of synaptic plasticity via the fusion of reinforcement learning
and unsupervised learning in neural networks [0.0]
In cognitive neuroscience, it is widely accepted that synaptic plasticity plays an essential role in our amazing learning capability.
With this inspiration, a new learning rule is proposed via the fusion of reinforcement learning and unsupervised learning.
In the proposed computational model, the nonlinear optimal control theory is used to resemble the error feedback loop systems.
arXiv Detail & Related papers (2023-03-26T12:18:03Z) - Minimizing Control for Credit Assignment with Strong Feedback [65.59995261310529]
Current methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals.
We combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization.
We show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using a learning rule fully local in space and time.
arXiv Detail & Related papers (2022-04-14T22:06:21Z) - Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent
Dynamical Systems [2.6084034060847894]
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases.
Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks.
We show that the proposed emphport-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest.
arXiv Detail & Related papers (2021-07-16T17:31:54Z) - Credit Assignment in Neural Networks through Deep Feedback Control [59.14935871979047]
Deep Feedback Control (DFC) is a new learning method that uses a feedback controller to drive a deep neural network to match a desired output target and whose control signal can be used for credit assignment.
The resulting learning rule is fully local in space and time and approximates Gauss-Newton optimization for a wide range of connectivity patterns.
To further underline its biological plausibility, we relate DFC to a multi-compartment model of cortical pyramidal neurons with a local voltage-dependent synaptic plasticity rule, consistent with recent theories of dendritic processing.
arXiv Detail & Related papers (2021-06-15T05:30:17Z) - Watch and learn -- a generalized approach for transferrable learning in
deep neural networks via physical principles [0.0]
We demonstrate an unsupervised learning approach that achieves fully transferrable learning for problems in statistical physics across different physical regimes.
By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems.
arXiv Detail & Related papers (2020-03-03T18:37:23Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.